On 23 Apr 2013, at 21:29, Brian Tenneson wrote:
Interesting read.
The problem I have with this is that in set theory, there are
several examples of sets who owe their existence to axioms alone. In
other words, there is an axiom that states there is a set X such
that (blah, blah, blah). How are we to know which sets/notions are
meaningless concepts? Because to me, it sounds like Doron's
personal opinion that some concepts are meaningless while other
concepts like huge, unknowable, and tiny are not meaningless. Is
there anything that would remove the opinion portion of this?
How is the second axiom an improvement while containing words like
huge, unknowable, and tiny??
quote
So I deny even the existence of the Peano axiom that every integer
has a successor.
I guess the author means that he denies the truth of the axiom of the
Peano axiom.
Eventually
we would get an overflow error in the big computer in the sky, and
the sum and product of any
two integers is well-defined only if the result is less than p, or
if one wishes, one can compute them
modulo p. Since p is so large, this is not a practical problem,
since the overflow in our earthly
computers comes so much sooner than the overflow errors in the big
computer in the sky.
end quote
What if the big computer in the sky is infinite?
Indeed.
Or if all computers are finite in capacity yet there is no largest
computer?
Indeed.
What if NO computer activity is relevant to the set of numbers that
exist "mathematically"?
Indeed.
Eventually it depends on the theory we start from. But to start the
reasoning in comp, we have to assume at least one universal system (in
the Church-Turing sense). If not, we don't get it. It remains a
logical possibility of using some physicalist ultrafinitism, but this
is heavy to only drop an explanation of the origin of consciousness/
physical--realities coupling. And by MGA + occam, unless there is
flaw, this cannot work with comp.
Bruno
On Monday, April 22, 2013 11:28:46 AM UTC-7, smi...@zonnet.nl wrote:
See here:
http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/real.pdf
Saibal
> To post to this group, send email to everyth...@googlegroups.com.
> Visit this group at http://groups.google.com/group/everything-list?hl=en
.
> For more options, visit https://groups.google.com/groups/opt_out.
>
>
>
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list?hl=en
.
For more options, visit https://groups.google.com/groups/opt_out.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
